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Factors of 1176

Factors of 1176 are numbers that, when multiplied in pairs give the product as 1176. There are 24 factors of 1176 of which 1176 itself is the biggest factor and its prime factors are 2, 3, 7 The Prime Factorization of 1176 is 23 × 31 × 72.

  • All Factors of 1176: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588 and 1176
  • Prime Factors of 1176: 2, 3, 7
  • Prime Factorization of 1176: 23 × 31 × 72
  • Sum of Factors of 1176: 3420
1. What Are the Factors of 1176?
2. Factors of 1176 by Prime Factorization
3. Factors of 1176 in Pairs
4. FAQs on Factors of 1176
Factors of 1176

What are Factors of 1176?

Factors of 1176 are pairs of those numbers whose products result in 1176. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1176?

To find the factors of 1176, we will have to find the list of numbers that would divide 1176 without leaving any remainder.

  • 1176/24 = 49; therefore, 24 is a factor of 1176 and 49 is also a factor of 1176.
  • 1176/588 = 2; therefore, 588 is a factor of 1176 and 2 is also a factor of 1176.
Similarly we can find other factors. Hence, the factors of 1176 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176.

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Factors of 1176 by Prime Factorization

The number 1176 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1176. The first step is to divide the number 1176 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1176 ÷ 2 = 588
  • 588 ÷ 2 = 294
  • 294 ÷ 2 = 147

Further dividing 147 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 147 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1176 can be written as 23 × 31 × 72 where 2, 3, 7 are prime.

 

Factors of 1176 in Pairs

Pair factors of 1176 are the pairs of numbers that when multiplied give the product 1176. The factors of 1176 in pairs are:

  • 1 × 1176 = (1, 1176)
  • 2 × 588 = (2, 588)
  • 3 × 392 = (3, 392)
  • 4 × 294 = (4, 294)
  • 6 × 196 = (6, 196)
  • 7 × 168 = (7, 168)
  • 8 × 147 = (8, 147)
  • 12 × 98 = (12, 98)
  • 14 × 84 = (14, 84)
  • 21 × 56 = (21, 56)
  • 24 × 49 = (24, 49)
  • 28 × 42 = (28, 42)

Negative pair factors of 1176 are:

  • -1 × -1176 = (-1, -1176)
  • -2 × -588 = (-2, -588)
  • -3 × -392 = (-3, -392)
  • -4 × -294 = (-4, -294)
  • -6 × -196 = (-6, -196)
  • -7 × -168 = (-7, -168)
  • -8 × -147 = (-8, -147)
  • -12 × -98 = (-12, -98)
  • -14 × -84 = (-14, -84)
  • -21 × -56 = (-21, -56)
  • -24 × -49 = (-24, -49)
  • -28 × -42 = (-28, -42)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1176 Solved Examples

  1. Example 1: How many factors are there for 1176?

    Solution:

    The factors of 1176 are too many, therefore if we can find the prime factorization of 1176, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 1176 = 23 × 31 × 72
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (2 + 1) = 4 × 2 × 3 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 1176 and 866.

    Solution:

    The factors of 1176 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176 and factors of 866 are 1, 2, 433, 866.

    Therefore, the Least Common Multiple (LCM) of 1176 and 866 is 509208 and Highest Common Factor (HCF) of 1176 and 866 is 2.

  3. Example 3: Find if 4, 6, 24, 56, 98, 137, 294 and 1176 are factors of 1176.

    Solution:

    When we divide 1176 by 137 it leaves a remainder. Therefore, the number 137 is not a factor of 1176. All numbers except 137 are factors of 1176.

  4. Example 4: Find the product of all the prime factors of 1176.

    Solution:

    Since, the prime factors of 1176 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

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FAQs on Factors of 1176

What are the Factors of 1176?

The factors of 1176 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176 and its negative factors are -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -49, -56, -84, -98, -147, -168, -196, -294, -392, -588, -1176.

What is the Sum of Factors of 1176?

Sum of all factors of 1176 = (23 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (72 + 1 - 1)/(7 - 1) = 3420

What are Prime Factors of 1176?

The prime factors of 1176 are 2, 3, 7.

What is the Greatest Common Factor of 1176 and 544?

The factors of 1176 and 544 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176 and 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544 respectively.

Common factors of 1176 and 544 are [1, 2, 4, 8].

Hence, the GCF of 1176 and 544 is 8.

What are the Common Factors of 1176 and 467?

Since, the factors of 1176 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176 and factors of 467 are 1, 467. Hence, 1176 and 467 have only one common factor which is 1. Therefore, 1176 and 467 are co-prime.

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